The main application I have for this is the turnover that you suggest, except that I use head down and shoulder up. I can also see it working as a bad armbar. Bad because it's too easily escaped but it would teach the principle well.

It is very similar to motions in Hangetsu. After the first turn you have three motions where one palm rises and the other drops. They remain parallel to the floor. The difference is that the Chung Gun, the dropping one has fingers pointing to the outside instead of forwards.

Just watched Hangetsu on youtube and I'd say an application for the motion in that kata could easily cross over into the similar TKD technique. They are identical but similar enough IMHO. I wonder if Gen. Choi had seen someone doing Hangetsu when he formulated Joong gun (and other patterns like Kwang Gae that uses that technique).

If we focus on the principles being demonstrated rather than the visual aspect of a technique then you may see this application at the beginning of Pinan/Heian Sandan, about half way through Pinan/Heian Yodan(the arm rotation that leads to a front kick and dropping elbow), the same motion in Kushanku, and the ''reinforced block'' found in Naihanchi/ Tekki Shodan.

FWIW - I have this (mainly) as an elbow break (palms pressing eitherside of the elbow joint), with the preceeding moves setting it up. The 2nd set is used to lock the arm behind the back, following the lock/break!